Question

limit

Answer 1

\[\lim_{x \rightarrow 1}\frac{ \sqrt[3]{x}-1 }{ \sqrt[4]{x}-1 }\]

Answer 2

familiar with L'hopital rule?

Answer 3

no

Answer 4

I tried substitution but it does not work

Answer 5

is there any way you can do it without the rule

Answer 6

yes

Answer 7

hmm yes.. what is the highest possible power of x that can be in your question?

Answer 8

so mulriply and divide by x-1
a=1

Answer 9

\(\huge\lim_{x \rightarrow a}\frac{ {x^n}-a^n}{ x-a }=na^{n-1}\)

Answer 10

n=1/3 in numerator and 1/4 in denom.

Answer 11

could we first try with \[t^3=\sqrt[3]{x}\]

Answer 12

not required, i think...

Answer 13

\[\frac{ (x^{1/3}-1)(x-1) }{ (x^{1/4} -1)(x-1)}\]

Answer 14

more like
\(\huge \frac{\frac{x^{1/3-1}}{x-1}}{\frac{x^{1/4}-1}{x-1}}\)

Answer 15

don't multiply them out, bring it in the form as i shown

Answer 16

then just use formula in num and denom

Answer 17

okay

Answer 18

\[\frac{ (x^{1/9}-1)(x^{2/9}+x^{1/9}+1) }{ (x^{1/8}-1)(x^{1/8}+1) }\]
I think

Answer 19

what the ... ?

Answer 20

ohhh sorry I am supposed to use the rule above not factorise

Answer 21

plz go through my comments....

Answer 22

\[\frac{ 1/3x^{-2/3} }{ 1/4x^{-3/4} }\]
then limit becomes\[\frac{ 1/3 }{ 1/4 }=4/3\]

Answer 23

thats good now :)

Answer 24

doubts ?

Answer 25

the formular you used looks like the derivaetive rule

Answer 26

according to formula its
\(\huge \frac{ 1/3 (1)^{-2/3} }{ 1/4(1)^{-3/4} }\)

Answer 27

or binomial

Answer 28

it is.....i don't know whether u can use it directly here....

Answer 29

thanks now I get it so does not depend on the value we are approaching

Answer 30

it does,
\(\huge\lim_{x \rightarrow a}\frac{ {x^n}-a^n}{ x-a }=na^{n-1}\)
the limit depends on a

Answer 31

here fortumately a=1

Answer 32

yes it is really helpful I will call it L'Hartnn rule

Answer 33

thanks

Answer 34

lol! :P
welcome ^_^

Answer 35

if we let \[x=t^{12}\]\[\frac{ t^4-1 }{ t^3-1 }=\frac{ (t-1)(t+1)(t^2+1) }{ (t-1)(t^2+t+1) }=\frac{ (t+1)(t^2+1) }{ t^2+t+1 }\]
\[\frac{ 2(2) }{ 1+1+1 }=4/3\]